# To "combine" functions in javascript in a functional way?

heritage

This is a concept from maths called function composition.

       f(x) = y
g(y) = z

g(f(x)) = z

(g•f)(x) = z


That last line is read "g of f of x equals z". What's great about composed functions is the elimination of points. Notice in g(f(x)) = z we take an x input and get a z output. This skips the intermediate point, y.

Composition is a great way to create higher-order functions and keep your code sparkly clean. It's plain to see why we'd want this in our Javascript programs.

comp

JavaScript is a multi-paradigm language with rich support for functions. We can create a simple comp function, which combines two input functions, g and f, and results in a new function -

function triple(x) {
return x * 3
}

function plusOne(x) {
return x + 1
}

function comp(g, f) {
return function(x) {
return g(f(x))        // "g of f of x"
}
}

const myfunc =
comp(triple, plusOne)

console.log(myfunc(1))

Evaluation

triple(plusOne(1))
triple(2)
6


compose

Just as the question suggests, it's likely we will want to combine more than two functions. Below we write compose which takes all of the input functions and reduces them using our simple comp from above. If no functions are given, we return the empty function, identity -

const triple = (x) =>
x * 3

const plusOne = (x) =>
x + 1

const comp = (g, f) =>
x => g(f(x))                     // "g of f of x"

const identity = (x) =>
x

const compose = (...all) =>
all.reduce(comp, identity)

const myfunc =
compose(triple, triple, plusOne) // any amount of funcs

console.log(myfunc(1))

Evaluation

triple(triple(plusOne(1)))
triple(triple(2))
triple(6)
18


pipe

You can be as creative as you like. Below, we write pipe which allows our programs to read in a comfortable left-to-right direction -

const triple = (x) =>
x * 3

const plusOne = (x) =>
x + 1

const pipe = x =>
f => pipe(f(x))

pipe(1)(plusOne)(triple)(triple)(console.log)           // 18
pipe(3)(triple)(plusOne)(triple)(plusOne)(console.log)  // 31

Evaluation of expression one -

f => pipe(f(1))
pipe(plusOne(1))
f => pipe(f(2))
pipe(triple(2))
f => pipe(f(6))
pipe(triple(6))
f => pipe(f(18))
pipe(console.log(18))
18


and expression two -

f => pipe(f(3))
pipe(triple(3))
f => pipe(f(9))
pipe(plusOne(9))
f => pipe(f(10))
pipe(triple(10))
f => pipe(f(30))
pipe(plusOne(31))
f => pipe(f(31))
pipe(console.log(31))
31


related techniques

Curried functions and partial application are concepts that gel with function composition. pipe above is introduced in another Q&A as $ and demonstrated again here - const$ = x =>           // "pipe", or whatever name you pick
k => $(k (x)) const add = x => y => // curried add x + y const mult = x => y => // curried mult x * y$ (1)                    // 1
(add (2))              // + 2 = 3
(mult (6))             // * 6 = 18
(console.log)          // 18

\$ (7)                    // 7
(add (1))              // + 1 = 8
(mult (8))             // * 8 = 64
(mult (2))             // * 2 = 128
(mult (2))             // * 2 = 256
(console.log)          // 256